Traditionally, the channel reciprocity is utilized in time division duplex (TDD) massive MIMO systems to reduce the cost of downlink channel estimation as long as the uplink CSI is obtained.
For frequency division duplex (FDD) massive MIMO, the compressive algorithms that exploit the sparsity of channel in angle domain have been used to estimate CSI.
However, the performance of compressive sensing is restricted with the linear sparsity assumption that does not accurately match the complex nonlinear sparse characteristics of the environment. Recently, Alkhateeb et al. revealed the deterministic relationship among different channels at different antennas and frequency bands, and introduced a new concept, namely the channel mapping in space and frequency domain [1]}. With a similar principle, Esswie et al. proposed a spatial channel estimation scheme to reconstruct the downlink channel from uplink channel measurements for FDD MIMO systems [2]}. In [3]}, Ali et al. constructed the channel covariance of the mmWave link from the spatial characteristics of the sub-6 GHz band.
